{"as_of":"2026-08-13T09:22:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:59accd68686445783b6e57c174ffc5dd98442d3c86c225dd64301b79a01a9ad8","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T05:19:14.014956Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-12T11:01:30.216099Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1009.4322","last_updated":"2010-09-22T10:36:25Z","snapshot_observed_at":"2026-07-06T02:15:46.182819Z","submitted_at":"2010-09-22T10:36:25Z","title":"A Simple Proof of Thue's Theorem on Circle Packing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1009.4322","snapshot_observed_at":"2026-08-12T05:19:14.014956Z","title":"Chang and L.-C","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2412.00601","last_updated":"2024-12-17T18:29:11Z","snapshot_observed_at":"2026-08-12T19:24:29.137554Z","submitted_at":"2024-11-30T22:26:38Z","title":"Sphere Packing on a Quantum Computer for Chromatography Modeling","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T05:19:14.014956Z"},"links":{"cited_paper":"/paper/1009.4322","citing_paper":"/paper/2412.00601"},"observation_digest":"sha256:3c655f301e4973b1d9b052ec432f3b778fe27338bd5659c18cc31211958d2100","observation_id":"057eb6f2-9d63-4b43-bc7c-d94e26293f6d","resolution":{"observed_at":"2026-08-12T05:19:14.014956Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1009.4322","last_updated":"2010-09-22T10:36:25Z","snapshot_observed_at":"2026-07-06T02:15:46.182819Z","submitted_at":"2010-09-22T10:36:25Z","title":"A Simple Proof of Thue's Theorem on Circle Packing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1009.4322","snapshot_observed_at":"2026-08-07T15:45:20.161603Z","title":"Chang and L.-C","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2505.14110","last_updated":"2026-06-25T09:23:59Z","snapshot_observed_at":"2026-08-10T15:33:00.800056Z","submitted_at":"2025-05-20T09:18:09Z","title":"On Dense Tetrahedra in Binary Sphere Packings","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:20.161603Z"},"links":{"cited_paper":"/paper/1009.4322","citing_paper":"/paper/2505.14110"},"observation_digest":"sha256:89c04332615e22d5e253854d16acdad4b4042c13f44f4eaffd99379a7cfa90b1","observation_id":"d9d16cdb-25eb-46ff-ad6f-3381a58f364d","resolution":{"observed_at":"2026-08-07T15:45:20.161603Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1009.4322","last_updated":"2010-09-22T10:36:25Z","snapshot_observed_at":"2026-07-06T02:15:46.182819Z","submitted_at":"2010-09-22T10:36:25Z","title":"A Simple Proof of Thue's Theorem on Circle Packing","version":1},"cited_work":{"arxiv_id":"1009.4322","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1009.4322","snapshot_observed_at":"2026-07-04T17:34:06.323859Z","title":"A simple proof of thue’s theorem on circle packing","venue":null,"work_id":"69a8f05b-ce72-4f48-9c9d-5d20a64bef5a","year":2010},"citing_paper":{"arxiv_id":"2605.03565","last_updated":"2026-05-05T09:39:14Z","snapshot_observed_at":"2026-07-06T23:16:30.147006Z","submitted_at":"2026-05-05T09:39:14Z","title":"Neural optimization for quantum architectures: graph embedding problems with Distance Encoder Networks","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-07T17:21:56.801163Z"},"links":{"cited_paper":"/paper/1009.4322","citing_paper":"/paper/2605.03565"},"observation_digest":"sha256:f276ea0a19f72e43bfc922e1ae27470c8e31afcb6a86aaff4f945cc0e5fbd1f1","observation_id":"1b4d596e-cfce-479c-b403-9024739775c1","resolution":{"observed_at":"2026-07-04T17:34:06.323859Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1009.4322","last_updated":"2010-09-22T10:36:25Z","snapshot_observed_at":"2026-07-06T02:15:46.182819Z","submitted_at":"2010-09-22T10:36:25Z","title":"A Simple Proof of Thue's Theorem on Circle Packing","version":1},"cited_work":{"arxiv_id":"1009.4322","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1009.4322","snapshot_observed_at":"2026-07-04T17:34:06.323859Z","title":"A simple proof of thue’s theorem on circle packing","venue":null,"work_id":"69a8f05b-ce72-4f48-9c9d-5d20a64bef5a","year":2010},"citing_paper":{"arxiv_id":"2605.04736","last_updated":"2026-05-06T10:34:52Z","snapshot_observed_at":"2026-08-11T02:16:52.794741Z","submitted_at":"2026-05-06T10:34:52Z","title":"Neural-powered unit disk graph embedding: qubits connectivity for some QUBO problems","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-08T17:30:54.314708Z"},"links":{"cited_paper":"/paper/1009.4322","citing_paper":"/paper/2605.04736"},"observation_digest":"sha256:0b81bc07600aec6efdd9bc25ae9d664d487b138e7cb263fb2c185942cf76e1dc","observation_id":"37735b9b-8100-467e-99c2-0f12bb304911","resolution":{"observed_at":"2026-07-04T17:34:06.323859Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1009.4322/citation-record","integrity":"/paper/1009.4322/integrity","json":"/paper/1009.4322/citation-record.json","paper":"/paper/1009.4322"},"outbound":[],"paper":{"arxiv_id":"1009.4322","last_updated":"2010-09-22T10:36:25Z","latest_version":1,"primary_category":"math.MG","snapshot_observed_at":"2026-07-06T02:15:46.182819Z","submitted_at":"2010-09-22T10:36:25Z","title":"A Simple Proof of Thue's Theorem on Circle Packing"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:1009.4322."}